It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that a woman came to the Prophet (peace and blessings be upon him) and said: My mother vowed to perform Hajj, and she died before performing Hajj. Shall I perform Hajj on her behalf? He (peace and blessings be upon him) said: "Yes, perform Hajj. What do you think: if your mother had owed a debt, would you have paid it?" She said: Yes. He (peace and blessings be upon him) said: "Pay the debt of Allah, for fulfilling it is more deserving."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الوصايا / 12602